PROCEEDINGS OF THE I.R.E.

Meteoric Echo Study of Upper Atmosphere Winds*L. A. MANNINGt, ASSOCIATE, IRE, 0. G. VILLARD, JR.t, ASSOCIATE, IRE, AND A. M. PETERSONt

Summary-A method is developed for measuring the velocity ofwinds in the 90- to 110-kilometer height region of the upper at-mosphere. From the Doppler frequency shift imparted to a con-

tinuous-wave reflection from a meteoric ionization column, a meas-

ure of the wind drift of the trail is found. Statistical analysis enablesaverage wind velocities to be measured to within perhaps 20 per

cent, and direction to 200, in a period of one or two hours. Observa-tions made during the early morning hours in the summer of 1949show typical average wind velocities to be 125 kilometers per hour,with motions from south-southwest and north the most common.

On some occasions, evidence of a nonuniform wind structure isfound.

N RECENT YEARS a steadily increasing interestin the properties of the upper atmosphere has high-lighted the need for knowledge of the wind systems

in the ionosphere. Such information has long been de-sired by students of terrestrial magnetism and iono-spheric physics, and it is now becoming of importance tomilitary planners as well.Measurements of winds at altitudes well above the

range of the sounding balloon have been difficult andrestricted to chance occurrence. Observation of the con-

tortion and drift of the luminous trains left by excep-

tionally bright meteors has enabled a few estimates ofair movements to be made at widely separated timesand geographical locations. The fortuitous nature of theevent and the difficulty of accurate triangulation re-

strict the usefulness as well as the accuracy of thesemeasurements.i 2 Again, wind information has been ob-tained by noting the drift of the exceptionally rare

noctilucent clouds. These clouds occur only at an alti-tude of 82 kilometers, and are seen only at high lati-tudes.3 More recently, two methods of studying windmotions by radio observations have been discussed inthe literature. Ferrell4 has described measurements ofthe drift of clouds of sporadic-E ionization as a possiblemeans for the study of wind motions at altitudes ofabout 120 kilometers. Such measurements are madepossible by the co-operative efforts of many hundreds ofamateur radio operators who report sporadic-E-propa-gated contacts. It remains to be demonstrated that thedrift which is observed is a wind drift rather than a mo-

*Decimal classification: R113.415 XR248. Original manuscriptreceived by the Institute, January 16, 1950. This work was supportedjointly by the Navy Department Office of Naval Research and theU. S. Army Signal Corps under ONR Contract N6-ONR-251Consolidated Task No. 7.

t Electronics Research Laboratory, Stanford University, Stan-ford, Calif.

1 C. P. Olivier, "Long enduring meteor trains," Proc. Amer. Phil.Soc., vol. 85, pp. 93-135; January, 1942.

2 C. P. Olivier, "Long enduring meteor trains," second paper,Proc. Amer. Phil. Soc., vol. 91, pp. 315-327; October, 1947.

3 C. Stormer, "Height and velocity of luminous night clouds ob-served in Norway, 1932," Vid. -Akad. Avh. I. M.-N. Ki., no. 2;1933.

4 0. P. Ferrell, "Upper atmosphere circulation as indicated bydrifting and dissipation of intense sporadic-E clouds," PROC. I.R.E.,vol. 37, p. 879; July, 1948.

tion of the causative agent or condition which causes theionization to become concentrated in sporadic-E clouds.Another method of wind measurement, applicable toheights in the E region, has recently been disclosed byMitra.1 It is based upon recording the rate of fading ofsignals which have been reflected from an irregular mov-ing ionosphere. The method has the advantage thatwinds are determined in a single experiment which is toa large extent under the control of the operator. It hasnot been shown, however, that the presence of theearth's magnetic field does not cause the electron windmeasured by this experiment to differ in direction andmagnitude from the true wind, consisting of an averagemotion of neutral molecules.

In the present paper is described a new method forexperimentally determining wind direction and velocityin the 80- to 110-kilometer height region of the upper at-mosphere. The method does not depend upon any spe-cial assistance in the form of unusual or hard-to-ob-serve phenomena, and is capable of supplying informa-tion on a region ol the atmosphere which has not as yetbeen studied on a regular basis.

THE METEOR ECHOES

The tools or probes used in the wind investigation areionization columns created in the lower ionosphere bythe passage of meteors.6'7 Upon entering this region,even relatively small particles create cylinders of ioniza-tion whose lengths are measured in tens of kilometers,but whose radii are a thousand times smaller. In thepresence of winds it is to be expected that these thin,short-lived columns are transported with a translationalvelocity which may be detected by radio echo means.We shall first outline the conditions under which suchechoes are detected, and then investigate the specialproperties the echoes should exhibit when winds areconsidered.

Because the ionization produced by the passage of ameteor is distributed along what amounts to a line, thestrength of the reflected signal from the column is veryaspect sensitive. In the majority of instances an echocan be received only when the trail is perpendicular to aray from the observatory. Immediately upon the pas-sage of the meteor, a "burst" of reflected signal is re-ceived, lasting typically for a second or so until the ioni-zation has been dissipated. Fig. 1 illustrates the geome-try of the reflection, and a sketch of received signal am-

5 S. N. Mitra, "A radio method of measuring winds in the iono-sphere," Part III, Jour. IEE, vol. 96, pp. 441-446; September, 1949.

6 L. A. Manning, "The theory of the radio detection of meteors,"Jour. Appl. Phys., vol. 19, pp. 689-699; August, 1948.

7 L. A. Manning, 0. G. Villard, Jr., and A. M. Peterson, "RadioDoppler investigation of meteoric heights and velocities," Jour.Appl. Phys., vol. 20, pp. 475-479; May, 1949.

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PROCEEDINGS OF THE I.R.E.

(a)ECHOAMaP-rruf D WWKC-IION

/ _ : £~~~~~F:FSCTr

r , \~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~2

IMtL IN SOt4n"-

(b)Fig. 1-(a) Geometry of reflection. (b) Typical amplitude of

reflected signal.

plitude versus time as typically observed. The fluctua-tions in amplitude of the echo noted just after the initialrise result from diffraction effects as the trail forms to itsfull length, and are a measure of the velocity of themeteor.8

TIME Nt4 eECONDOS

Fig. 2-Beat between transmitted continuous wave and echofrom moving column.

DOPPLER SIIIFT CAUSED BY A UNIFORM WINDAssume that a uniform upper atmosphere wind exists

which is everywhere the same in direction and velocity.We may then examine the Doppler shift such a windwill produce upon a particular meteor reflection, as afunction of the position of the meteor. Set up a rectangu-lar co-ordinate system with z the vertical co-ordinate,and so rotated that the wind vector lies in the y-z plane.The wind velocity w may then be expressed as a spacevector as follows:

w = jw cos a - kw sin a(

EFFECTS OF WINDS UPON ION TRAILS

On the basis of earlier investigations there is reason tosuspect the existence of winds having velocities some-where between zero and 600 kilometers per hour atmeteoric heights. We shall first suppose the existence ofsuch winds, then investigate what effects they may beexpected to have upon meteor echoes, and finally showhow the nature of the winds may be deduced from theecho effects. Due to wind drift alone, there should be nochange in the amplitude of the reflections, since the trailwill drift little more than a tenth of one per cent of thedistance to the observatory in a second. If we examinethe radio-frequency phase of the received echo, however,we shall find that whenever the reflector moves towardsthe observatory by half a wavelength, there will be a full-cycle shift in the reflected wave. The reflection from theelectron cloud can be shown to be analogous in this re-spect to the reflection from a metallic reflector. Bybeating the echo with a portion of the transmitted sig-nal, it is possible to detect motion of the reflector interms of cyclic fluctuations of the resultant signal. InFig. 2 is sketched an echo from a target which has movedalmost three half-wavelengths in the duration of the re-flection, with a velocity of one-half wavelength per sec-ond. The preliminary high-frequency fluctuation isknown as a "meteor whistle," and, like the diffractionfluctuations, is a measure of the velocity of the meteoricparticle which formed the column.7 This velocity shouldnot be confused with the much slower wind drift of thefully formed trail. The low beat frequency exhibited inFig. 2 is called a "body Doppler." At a wavelength of tenmeters, a radial drift velocity of 100 kilometers per hourwould produce a body Doppler of 5.5 cps.

8 C. D. Ellyett and J. G. Davies, "Velocity of meteors measuredby diffraction of radio waves from trails during formation," Nature,vol. 161, pp. 596-597; April 17, 1948.

where a is the dip angle of the wind with respect to the- >*

horizontal, and j and k are unit vectors in the y and zdirections. If we now call r the position vector of themeteor with respect to an origin at the observatory, thecomponent v of the trail drift velocity towards the ob-servatory will be

r -*

v = -w (2)

where r, the magnitude of the position vector, is therange. Using the notation that h is the column altitude,p the horizontal distance from the observatory, and 0 the

k

s. 0 NK PL9.) VIEW

Fig. 3-Co-ordinates of the ionization column.

angle between the projections of r and w in the horizon-tal plane, as in Fig. 3, we find

r> > jr = ip sin 6 + jp cos 6 + kkl (3)

where i is the unit vector in the x direction; so that, us-ing (2), and the relation p= (r2-h2)'1,2 we find that

v = w[I -(hl/r)2] 12 cos a cos 0 - w(h/r) sin a (4)

for the radial velocity of the reflection point.It will be seen that the Doppler shift for a uniform

wind varies sinusoidally with the bearing angle 0 of the

878 A u>gust

i

(1)

_;1

Manning, Villard, and Peterson: Meteoric Echo Study of Upper Atmosphere Winds

observed meteor, thus suggesting a statistical means fordetermining the direction of an average wind motion. Inparticular, if the Doppler shift F, related to the radialvelocity v by

2vF= - (5)

where X is the wavelength, be determined for manymeteors distributed at random about the observatory,the wind direction will correspond to the azimuth forwhich the largest average negative (receding) shift F isobtained, provided that h/r is independent of 0. Fig. 4 isa plot of (5), with v determined from (4), for an as-

Fourier analysis of the observed F's versus 0 will yieldthe coefficient

-2w p=N [-(h)n1/-E 1l-(-]XN n=1 - 'rn-

Designating the Fourier amplitude of the cosine-&variation of observed shift by A, the wind speed is

X Nw = -A

2 n=N [ 2 1/2

n=l n

(8)

Analysis of typical nonshower records has shown thelast factor in (8) to be substantially independent of azi-muth, and to have a value of the order of 4/3. For mostaccurate results, however, the summation should beperformed from the actual data.

EXPERIMENTAL VERIFICATION OF THE THEORY

Using equipment to be described in the next section,it has been possible to obtain experimental results whichare consistent with the previously developed theorybased on the assumption of a uniform average wind.

Fig. 4-Theoretical variation of Doppler shift (radial velocity)with azimuth.

sumed h/r of 0.7, and a dip angle of 200 in (4). It will be 0 inoted that under these conditions the average value of oDoppler frequency is displaced by an amount dependentupon the dip angle of the average wind. If h/r=0.7, dis- aplacement may be expressed as a fraction of the sine 5amplitude A simply as lb.

zD 0

- = tan a (6) u

AIwhere D/A is the fractional displacement.

PROCEDURE FOR WIND ANALYSISAssume that meteors have been detected in many di-

rections at known ranges r, and that for each of the me-teors the velocity of approach or recession v has been de-termined. For practical reasons the directions 0 may bedetermined only to within one of some number of sec-tors, say the 16 points of the compass. It is then possibleto find the average radial velocity v in each given sector,and to plot this average velocity, or the average Dopplershift F, versus direction. In accordance with (4) and (5)the value of F for a given sector Om. assuming a =0, is

2w n=1 rn) -

= - 2w cos Am | --[ (h(7)X N

where N observations are made in the sector of directionAm. To the extent that the summation is independent of0, which is to say that the range distribution of the ob-served meteors is independent of azimuth, the averageobserved Doppler shift will vary sinusoidally with 0, and

Fig. 5-Average body-Doppler frequency F versus direction onSeptember 11, 1949.

In Fig. 5 is shown a plot of average body-Doppler fre-quency versus direction as obtained experimentally.Fourier analysis of these ordinates can be made to de-termine the direction and magnitude of the wind. Thewind comes from the direction corresponding to the pos-itive peak of the best-fitting sine wave.Study of many plots such as that in Fig. 5 has shown

that the constant displacement term D in the Fourieranalysis tends to be less than the sine amplitude A by aratio of eight or more to one, the ratio increasing whenlarger samples of data are used. Use of (6) then serves todemonstrate the average winds to be horizontal to with-in a few degrees.The importance of this observation is principally that

it excludes the possibility that the observed electroncloud drift is in any way different from that of the truewind. A difference could conceivably exist because of theeffect of the earth's magnetic field on electron motion. Ifthe electronic collision frequency is below the gyro fre-quency, electrons can move freely only parallel to the

1950 879

PROCEEDINGS OF THE I.R.E.

earth's field, so that in the absence of electric attractionto positive ions, the drift of electrons would not corre-spond to that of the true wind, but rather to the com-ponent of the true wind in the direction of the magneticfield. Calculation shows that the electron collision fre-quency equals the gyro frequency at about 100 kilo-meters,9"10 which is in the neighborhood of meteoric re-flection heights. Having shown the electron drift to behorizontal within a few degrees, while the magnetic dipis about 650, we have shown that magnetic effects do notimpair the accuracy of the wind determination. It maybe noted that the height at which the ionic collision fre-quency equals the ionic gyro frequency is about 130 to150 kilometers. Above this height positive and negativecharges will drift in the magnetic-field direction, whilein the intermediate altitude range of the E layer carefulstudy will be needed to determine what resultant mo-tion the ionization acquires. The wind velocity deter-minations described by Mitra,5 which are based uponfading rates in the E layer, appear to depend on elec-tron drift in this intermediate region. Experimentalproof that his observed winds are not affected by theearth's magnetic field wxould be reassuring.

EXPERIMENTAL EQUIPMENT

The Doppler recordings of reflected signal that havebeen used in the wind studies have been made usingcontinuous-wave emissions of approximately 1-kilowattpower at a frequency of 23.1 Mc. In addition, a pulsedtransmitter has been operated at 17.3 Mc for range de-terminations. In a previous paper the authors have de-scribed some of the techniques involved in receiving andrecording the echoes.7 For wind studies the system de-scribed previously must be augmented by a directionfinder, and by a sense indicator which will determinewhether the received signal is shifted to a frequency afew cycles above or below that transmitted.

Ordinary direction finders are not adapted for meteo-ric work because a meteor echo is a relatively weak sig-nal of very short duration. In order to determine suc-cessfully a meteor's bearing, a direction finder is neededwhich will distinguish the received signals in terms ofrange, and will give a positive, instantaneous indicationof direction involving no sense ambiguity. A specialmeteor direction finder was constructed which providesthe needed features. An electronically sweeping antennapattern is obtained by using an array of four verticalantennas spaced about a vertical reflector. Each antennathen radiates principally to a single quadrant, and theiroutputs are amplified by four sinusoidally gated pre-amplifiers before being combined and amplified by a re-ceiver of ordinary design. Effectively, a single rotating

I E. F. George, "Electronic collisional frequency in the upperatmosphere," PROC. I.R.E., vol. 35, pp. 249-256; March, 1947.

10 G. Grimminger, "Analysis of Temperature, Pressure, andDensity of the Atmosphere Extending to Extreme Altitudes," ProjectRAND Report No. R-105 Douglas Aircraft Co., Inc., November 1,1948.

beam is obtained. The presentation involves sixteenseparate A-scope range patterns all displayed on a sin-gle sweep. Fig. 6 shows the appearance of the resultantoscilloscope pattern.

Fig. 6-Direction-finder presentation.

During a single sweep the antenna pattern is causedto go through one revolution, and it consequently modu-lates the envelope of the received pulse amplitudes asshown in the drawing. It has been found that echoes offractional-second duration can be measured with thisinstrument despite the presence of stronger reflectionsin other directions, because of the range resolution in thesixteen A-scope patterns. The eye is well able to deter-mine the largest of sixteen spikes arranged in this way.Polar presentations, on the other hand, were found to beextremely confusing.The problem of detecting the sign of a Doppler shift

of perhaps half a cycle per second superimposed upon a23-Mc carrier again required special methods for itssolution.

Consider Fig. 7, which is a vector plot of wave ampli-tude and phase relative to the transmitted wave. In thisplot the reflected-wave vector will not be stationary. Itwill revolve at the difference frequency corresponding

Fr24SW\TEt WAVL5"VFTFtED 90-

FLFsCT.D WN9SJI

\--rQkN4SmNTEbt WNI'v?

Fig. 7-Vector relationships in the sense detector.

to the Doppler shift, and the direction of rotation willcorrespond to the sign of the shift. When the reflectedwave is in phase with the transmitted wave, the beatwill have maximum amplitude. If, however, the re-flected wave is combined with a signal of transmittedfrequency but possessing a 900 phase lead, a beat will beobtained which is shifted 90° at the beat frequency. It isevident that for the phasing shown in Fig. 7, clockwiserotation of the reflected vector will cause the beat withthe shifted transmitted wave to lead the phase of thebeat with the unshifted transmitted wave. If the sign of

880 August

A1anning, Villard, and Peterson: Meteoric Echo Study of Upper Atmosphere Winds

the Doppler shift, and hence the rotation, is reversed,the beat will lead in the other channel. Fig. 8 shows

Fig. 8 Doppler beats demonstrating technique of determiningsign of shift.

beats recorded using this principle, and clearly demon-strating a 90° phase shift enabling the sign of the Dop-pler shift to be determined.

FURTHER CHARACTERISTICS OF THEDOPPLER SHIFT

We have, on the assumption that uniform averagewinds exist at meteoric heights, determined the effectthey should have upon meteoric echoes. A method ofmeasuring wind direction and velocity based on theseassumptions has been outlined, and experimental ob-servations are found to give results consistent with thetheory. It should be pointed out that other measurableproperties of the experimental Doppler shift are alsoconsistent with the wind interpretation.The wind theory predicts a body Doppler which will

have no systematic variation in beat frequency through-out the duration of an echo. Statistical study has dem-onstrated only random fluctuations in frequency duringthe life of an echo, so that no appreciable component ofvelocity may be accredited to an expansion-contractionprocess such as would be caused by trail diffusion. Whenthe Doppler shift for a given reflection is investigatedusing two carrier frequencies simultaneously, it is found

,0

10 LINE ow_3iOpL

1t-

5 X

A.

> 3 * / @~*

Or

#Z * / *.* 0

o /0

that the beat frequency is directly proportional to thecarrier frequency, as shown in Fig. 9. The velocity of thereflecting surface is hence not a function of the radiofrequency, as it might be if varying penetration into aiiionized cloud were involved. Further proof that horizoni-tal motion of the clouds is involved has been obtaineclby plotting body-Doppler frequency versus slant range.The observed increase of frequency with range is con-sistent with the geometry of reflection from a horizon-tally moving body.

DESCRIPTION OF OBSERVED WINDSOn about a dozen and a half occasionis during the sum-

mer of 1949, measurements of wind conditioins havebeen made. The hours prior to sunrise were selectecl forthe measurements because the lack of initerfering sig-nals and the maximum rate of meteoric arrival at thattime simplify the measurement problem. It was founidthat in a period of about two hours enough echoes couldbe obtained to determine the average wind conditioniswith good reliability. In Fig. 10 is shown a vector plot ofthe wind velocities and directions as determined bythese tests. It will be seen that south-southwest is themost favored direction during the period of observation,and that average velocities of 100 to 150 kilometers perhour are representative.

VEOATY fl4KM ~

w<

Fig. 10 Average upper-atmosphere wind velocities during the sum-mer of 1949, between 3 and 6 AM., local time, at Stanford Uni-versity, Stanford, Calif. Winds blow from indicated directions.

The winds which were found originating from thewest were especially interesting because of their low ap-parent speed and unusual direction. Examination of theDoppler frequency data for these days shows a largescatter in the observed shifts corresponding to a givenbearing. Both negative and positive shifts were found inprofusion in many sectors. The conclusion seems to bethat the wind motion was either very turbulent and

BO0f OOPPL!Q AI8NCTNT 30.G_ MC %N CP S

Fig. 9 Proportionality of body-Doppler frequency to carrierfrequency.

I

1950 881

PROCEEDINGS OF THE I.R.E.

changeable, or that it was blowing in two opposing di-rections in strata of different altitudes. It has been foundon several occasions that the occurrence of these "con-fused" winds correlates with the presence of diffusetraces in 100-kc vertical-incidence ionosphere sound-ings,1' but sufficient data have not yet been obtainedto establish the connection beyond all doubt.

If it is assumed that the "confused" echoes resultfrom observations wxith a fraction x of the meteors fall-ing in one stratum, then a fraction (1-x) will fall in theremaining layer. Fig. 11 demonstrates the resultantwind that will be determined by analyzing such data asthough all the reflections were in a single stratum. It willbe seen that the tip of the resultant vector lies along aline connecting the tip of the true wind vectors in thelayers involved. The same result would be obtained ifthere were only one stratum, and it is assumed that thewind blew first in one direction and then in another dur-ing the period of measurement.

Wa

PLAIN \I LV\

11-Resultant wind when observation is made in two strata.It will be seen that the tip of the resultant vector lies along aline connecting the tip of the wind vectors in the strata involved.

It might be of interest to point out that on most oc-casions the highest observed body-Doppler frequencycorresponds to a radial drift of the individual meteortrail of the order of three or four times the average (hori-zontal) wind velocity. Since both positive and negativeDoppler shifts are observed in each direction on a typi-cal night, it is seen that the instantaneous upper atmos-phere winds are clearly nonuniform and variable. Thisbehavior seems to be compatible with the observedrapid deformations of the visible trails left by exception-ally large meteors.

JTSE OF LEAST-SQUARE ANALYSISWhen an experimental plot of average body-Doppler

frequency versus direction is obtained, Fourier analysismay be used to determine the amplitude A of the sinus-oidal variation. It commonly occurs, however, that

100R. A. Helliwell, "Ionospheric virtual height measurements at

100 kilocycles." PROC. I.RE., vol. 37, pp. 887-894; August, 1949.

meteors do not arrive in random directions about anobserver. There is a tendency for meteors to strike theearth on its forward side in its orbit around the sun."2Because of the perpendicular nature of the reflectionprocess, this directional property appears also in thedistribution of observed echoes in azimuth. In those di-rections in which meteors are most plentiful the averagebody Doppler is determined with a much smaller statis-tical error than in the less favored directions. An ordi-nary Fourier analysis of the average body Doppler givesno weight to the better determined points. Conse-quently, a "weighted Fourier analysis" has been used inthe actual reductions. This analysis has been made byassuming the average displacement D to be zero, andthen seeking the amplitude of the sinusoidal variationwhich produces the least mean-squared deviation fromthe average ordinates, when the ordinates are given amultiplicity corresponding to the number of observa-tions. It can be shown that this formulation is equiva-lent to achieving the least mean-squared deviation fromthe individual experimental points. If all ordinates areevenly weighted, the present analysis reduces to a sim-ple Fourier analysis.

Let the equation of the best fitting sine variation bey = -A cos (d-4') where A is the desired amplitude, 4 isthe direction in which the wind blows, and 0 is the azi-muth at which the shift y is obtained. We shall then seekthe values of 4> and A which will minimize the error Egiven by

n=N

E2 = E, [A cos (,r- 4) + yn1]2n=l

(9)

where y,, is the experimental ordinate in sector n. Byminimizing E with respect to 4 and A, two simultaneousequations may be obtained in cos 4' and sin 4. Using, theabbreviation sin E-= s, cos £"=c

cos 4(AE c2) + sin 4(A>E cs) = - >3 YnCcos 4(A , cs) + sinl 4(A>E s2) = - 'ynS.

Solving for tan 4'

>3 C2 , ynS - >3 CS> ynCtan 4' -- -3 si yrC -

>SC

> ynSwhile the amplitude A is

A E ync[1 + tan2 4]'/2/1- cl+ tan O' sc

(10)

(11)

With the use of these formulas it is possible to obtainwind speeds and directions even when one or more sec-tors are completely deficient in data.

CONCLUSIONSA method has been developed for determining the

magnitude and direction of winds in the 90- to 100-kmheight region of the upper atmosphere. The method

12 Fletcher G. Watson, "Between the Planets," The BlakistonCompany, Philadelphia, Pa., p. 97; 1941.

882 A ugu st

PROCEEDINGS OF THE I.R.E.

is based upon measurement of the Doppler shift im-parted by the wind drift to reflections from meteoricionization columns. In the present stage of develop-ment, one or two hours of observation serve to specifyaverage velocities to within perhaps twenty per centand direction to better than twenty degrees. A scoreof measurements made during the summer of 1949have shown the average winds to be horizontal and tohave velocities of the order of 125 km. The mostusual direction was from south-southwest, with northsecond. Upon some occasions, record reduction basedupon the assumption of a single uniform wind yieldsan apparently low-velocity wind of intermediate di-rection. At these times, the average wind which is

measured is probably the resultant of intermittentwinds blowing in different directions at the same alti-tude, or of winds blowing in different directions at dif-fering altitudes. A suggestion of a correlation has beenobserved between the existence of such wind conditions,and diffuse traces in low-frequency ionosphere sounding.

Extension of the scope of the measurement programin order to investigate the diurnal, seasonal, and geo-graphic variations of the wind is desirable. Convenientmethods for measuring the height of the reflections arealso needed so that possible vertical stratification in thewind system may be investigated. The meteoric ioni-zation method is the first available for wind studies at 90to 100 km on any but a completely fortuitous basis.

Complex Dielectric-Constant Measurements inthe 100- to 1,000-Megacycle Range *

A. G. HOLTUM, JR.t, ASSOCIATE, IRE

Summary-A method is described wherein the dielectric constantand conductivity of lossy materials may be determined quickly andconveniently. A sample of the material is incorporated as the dielec-tric of a capacitor which acts as a load terminating a slotted measur-ing line. The complex impedance of this load can be determined bythe conventional method from the voltage standing-wave ratio andposition of the minimum. The inherent limitations of the methodrestrict its application to medium- and high-loss materials becauseof the very high standing-wave ratios encountered as the con-ductivity decreases. However, the dielectric constant alone maybe measured for low-loss materials.

Standardized components are used throughout, with the excep-tion of the sample holder.

I. INTRODUCTION

A MICROWAVE FREQUENCIES the dielectricproperties of nonconducting materials may bedetermined from the propagation characteristics

of an electromagnetic wave through the medium. Vari-ous methods of attacking this problem are discussed inthe literature, which includes an extensive bibliographyof recent work in this field.1

Application of these methods to the frequency rangefrom 100 to 1,000 Mc is in some cases feasible. Thesizes and shapes of the material sample required, how-ever, become cumbersome as the frequency is decreased.

Following suggestions in the literature, the details ofan alternative method have been worked out and ap-

* Decimal classification: R216.1. Original manuscript received bythe Institute, September 26, 1949; revised manuscript received,April 3, 1950.

t Signal Corps Engineering Laboratories, Fort Monmouth, N. J.1 C. G. Montgomery, "Technique of Microwave Measurements,"

Rad. Lab. Ser., vol. 11, McGraw-Hill Book Co, New York, N. Y.;1947.

plied. This method consists of incorporating the sam-ple, which is in the shape of a small disk, as the dielectricof a capacitor which acts as a load terminating a slottedcoaxial transmission line. The problem then becomes oneof simply measuring the terminating complex imped-ance, utilizing standard transmission-line techniques.The limitations of the method are obvious, inasmuch

as a measurable voltage standing-wave ratio would nec-essarily require the value of the equivalent parallel re-sistance to be close to the same order of magnitude asthe characteristic impedance of the measuring line. Thereal part of the dielectric constant may be determinedfor low-loss dielectrics, however, from the position of theminimum alone.

II. THEORY

The electromagnetic properties of any ordinary mate-rial, which is isotropic and homogeneous in the macro-scopic sense, can be completely specified by two complexconstants-the complex dielectric constant E, and thecomplex permeability ,uc. These can be expressed as fol-lows:

E, = ' -jE" = Eo k(1- j tan 8)Pc= -ijp'" = Puo (for nonmetallic materials),

(1)

(2)where c' is the real part of the dielectric constant, K isthe specific inductive capacity, C" is the loss factor, andu' and ,u" are the real and imaginary parts of the per-meabilitv.

k = C-/co and tan a = C"/CCo = dielectric constant of free space = 8.854 X 10-12

farads per meter

1950 883